OK, I can grasp the idea of space as a fabric. The analogy of a mass being like a weight on a trampoline, taken to 3D. I can get that.

I can't get this geometry of the universe thing. I mean, I can imagine the universe being a ball or toroid.... but flat? Flat, beyond 2D, implied a thickness, which implies a 3D object. (Likewise saddle-shaped.)
So in all these cases, there's an outer edge. Meaning, if one travel long enough you'll reach the edge. I don't buy that, and since I'm not an educated astrophysicist, the only answer is I have it wrong.

OK, parallel lines forever. I get that concept on the surface of a sphere. But, and here's the crux of why I don't get this geometry topic--we're not on the surface of an object! We're, in a manner of speaking, INSIDE the object. So, if I were to imagine myself inside a sphere, and shoot two parallel lines, yeah, they'll remain parallel...until the reach the edge. Likewise if I were some raisin in the middle of a bagel, the lines would reach an edge.
What then?

Does this make any sense? (Sometimes naive questions from ignorant people can be just as baffling as educated answers from smart people.)